The acquisition of spectral information for specimens has many practical applications. In many cases, acquiring this spectral information requires dividing a signal to be analyzed into a plurality of frequency ranges or “bins.” This division often produces signal levels that have poor signal-to-noise ratio, so that data acquisition requires long integration times. This is particularly challenging for specimens that require point by point scanning for evaluation. For example, electron energy loss spectra (EELS) often exhibit poor signal-to-noise ratio, limiting the usefulness of EELS. Such problems can be even more difficult in hyperspectral imaging that seeks high resolution both spatially and spectrally. The use of high power electron beams and long exposure times could permit improved signal-to-noise ratio in electron microscopy, but such exposures tend to alter specimen characteristics. New approaches to obtaining spectral information are needed.